I wanted to ask about interaction term. I am having an ordinal probit model. The two of the independent variables that i have are discrete 1-Uni( a 0,1 dummy variable) and second is continuity (1,2,3) likert scale variable. Is an interaction term of these two variables possible> I hope i have made it clear.

Another problem remains that if i introduce this interaction term (uni*continuity) it remains insignificant, and also makes the variable "uni" insignificant,


I have encountered this problem recently and have not found many sources which explain this so I thought I would answer. The interaction effect in a non-linear model is possible to compute but it is tricky as it is not equal to the marginal effect on the interaction term.

Say you have the probit model $E(y|x_1,x_2)=\Phi(\beta_1 x_1 + \beta_2 x_2 + \beta_{12} x_1 \times x_2)$ where $x_1$ is continuous and $x_2$ is discrete. Interpreting the marginal effect of the interaction term $\beta_{12} \Phi'(.)$ as the true interaction effect is incorrect (this would be true if we had a linear model).

If you take the second cross-partial derivative $\frac{\delta E^2(y|x_1,x_2)}{\delta x_1 \Delta x_2}$ you can find the interaction effect which is

$$=\dfrac{\delta E^2(y|x_1, x_2)}{\delta x_1 \Delta x_2} = \Phi ' (\beta_1 x_1 + \beta_2 + \beta_{12} x_1)(\beta_1 + \beta_{12}) - \Phi ' (\beta_1 x_1)(\beta_1) $$

which as you can see is different from $\beta_{12} \Phi'(.)$. Note that even in cases where your coefficient interaction term is 0, the true interaction effect might still be non zero. Ai & Norton (2002). The other problem with this non-linear interaction effect is that a standard t-test on the coefficient estimate doesn't work and other more advanced methods of calculating the standard errors must be used (see the paper for how they do it).

Ai & Norton (2003) have created a user-written STATA command inteff to visually plot the interaction effect but this is only available after Probit & Logit models unfortunately.

You could, if you are using STATA, calculate the marginal effects using the command margins, dydx(x1) ... at (x2 = 0(1)1) and this will give you the marginal effect when x2=1 and x2=0 which you can compare by supplementing pwcompare(effects) at the end of your code. This however would be the interaction effect for a specific value of your $x$s (The real interaction effect varies by individual as their $\Phi(.)$ changes).

Another way to represent the interaction effect is graphically and this is explained by Greene (2010).

| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.